--- rpl/lapack/lapack/dlanst.f 2010/08/06 15:28:40 1.3 +++ rpl/lapack/lapack/dlanst.f 2016/08/27 15:34:28 1.14 @@ -1,9 +1,109 @@ +*> \brief \b DLANST returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix. +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLANST + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* DOUBLE PRECISION FUNCTION DLANST( NORM, N, D, E ) +* +* .. Scalar Arguments .. +* CHARACTER NORM +* INTEGER N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION D( * ), E( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLANST returns the value of the one norm, or the Frobenius norm, or +*> the infinity norm, or the element of largest absolute value of a +*> real symmetric tridiagonal matrix A. +*> \endverbatim +*> +*> \return DLANST +*> \verbatim +*> +*> DLANST = ( max(abs(A(i,j))), NORM = 'M' or 'm' +*> ( +*> ( norm1(A), NORM = '1', 'O' or 'o' +*> ( +*> ( normI(A), NORM = 'I' or 'i' +*> ( +*> ( normF(A), NORM = 'F', 'f', 'E' or 'e' +*> +*> where norm1 denotes the one norm of a matrix (maximum column sum), +*> normI denotes the infinity norm of a matrix (maximum row sum) and +*> normF denotes the Frobenius norm of a matrix (square root of sum of +*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] NORM +*> \verbatim +*> NORM is CHARACTER*1 +*> Specifies the value to be returned in DLANST as described +*> above. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix A. N >= 0. When N = 0, DLANST is +*> set to zero. +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension (N) +*> The diagonal elements of A. +*> \endverbatim +*> +*> \param[in] E +*> \verbatim +*> E is DOUBLE PRECISION array, dimension (N-1) +*> The (n-1) sub-diagonal or super-diagonal elements of A. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date September 2012 +* +*> \ingroup auxOTHERauxiliary +* +* ===================================================================== DOUBLE PRECISION FUNCTION DLANST( NORM, N, D, E ) * -* -- LAPACK auxiliary routine (version 3.2) -- +* -- LAPACK auxiliary routine (version 3.4.2) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* November 2006 +* September 2012 * * .. Scalar Arguments .. CHARACTER NORM @@ -13,48 +113,6 @@ DOUBLE PRECISION D( * ), E( * ) * .. * -* Purpose -* ======= -* -* DLANST returns the value of the one norm, or the Frobenius norm, or -* the infinity norm, or the element of largest absolute value of a -* real symmetric tridiagonal matrix A. -* -* Description -* =========== -* -* DLANST returns the value -* -* DLANST = ( max(abs(A(i,j))), NORM = 'M' or 'm' -* ( -* ( norm1(A), NORM = '1', 'O' or 'o' -* ( -* ( normI(A), NORM = 'I' or 'i' -* ( -* ( normF(A), NORM = 'F', 'f', 'E' or 'e' -* -* where norm1 denotes the one norm of a matrix (maximum column sum), -* normI denotes the infinity norm of a matrix (maximum row sum) and -* normF denotes the Frobenius norm of a matrix (square root of sum of -* squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. -* -* Arguments -* ========= -* -* NORM (input) CHARACTER*1 -* Specifies the value to be returned in DLANST as described -* above. -* -* N (input) INTEGER -* The order of the matrix A. N >= 0. When N = 0, DLANST is -* set to zero. -* -* D (input) DOUBLE PRECISION array, dimension (N) -* The diagonal elements of A. -* -* E (input) DOUBLE PRECISION array, dimension (N-1) -* The (n-1) sub-diagonal or super-diagonal elements of A. -* * ===================================================================== * * .. Parameters .. @@ -66,14 +124,14 @@ DOUBLE PRECISION ANORM, SCALE, SUM * .. * .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME + LOGICAL LSAME, DISNAN + EXTERNAL LSAME, DISNAN * .. * .. External Subroutines .. EXTERNAL DLASSQ * .. * .. Intrinsic Functions .. - INTRINSIC ABS, MAX, SQRT + INTRINSIC ABS, SQRT * .. * .. Executable Statements .. * @@ -85,8 +143,10 @@ * ANORM = ABS( D( N ) ) DO 10 I = 1, N - 1 - ANORM = MAX( ANORM, ABS( D( I ) ) ) - ANORM = MAX( ANORM, ABS( E( I ) ) ) + SUM = ABS( D( I ) ) + IF( ANORM .LT. SUM .OR. DISNAN( SUM ) ) ANORM = SUM + SUM = ABS( E( I ) ) + IF( ANORM .LT. SUM .OR. DISNAN( SUM ) ) ANORM = SUM 10 CONTINUE ELSE IF( LSAME( NORM, 'O' ) .OR. NORM.EQ.'1' .OR. $ LSAME( NORM, 'I' ) ) THEN @@ -96,11 +156,12 @@ IF( N.EQ.1 ) THEN ANORM = ABS( D( 1 ) ) ELSE - ANORM = MAX( ABS( D( 1 ) )+ABS( E( 1 ) ), - $ ABS( E( N-1 ) )+ABS( D( N ) ) ) + ANORM = ABS( D( 1 ) )+ABS( E( 1 ) ) + SUM = ABS( E( N-1 ) )+ABS( D( N ) ) + IF( ANORM .LT. SUM .OR. DISNAN( SUM ) ) ANORM = SUM DO 20 I = 2, N - 1 - ANORM = MAX( ANORM, ABS( D( I ) )+ABS( E( I ) )+ - $ ABS( E( I-1 ) ) ) + SUM = ABS( D( I ) )+ABS( E( I ) )+ABS( E( I-1 ) ) + IF( ANORM .LT. SUM .OR. DISNAN( SUM ) ) ANORM = SUM 20 CONTINUE END IF ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN